Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afgw)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.afgw.01

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), -(15/4)}, z] == (1/(124804708875 z^(1/4))) (Sqrt[2] ((124804708875 - 220866515100 z + 32394978000 z^2 + 47880201600 z^3 + 16608049920 z^4 - 11524423680 z^5 + 46735294464 z^6 + 6102712320 z^7 + 16777216 z^8) BesselI[1/4, Sqrt[z]]^2 + 36 Sqrt[z] (13867189875 - 6051137400 z - 7990567200 z^2 - 2943494400 z^3 - 633937920 z^4 - 993607680 z^5 + 1345847296 z^6 + 29360128 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (124804708875 + 111946041900 z + 45649850400 z^2 + 13628260800 z^3 + 5861560320 z^4 + 3574333440 z^5 + 1330642944 z^6 + 4194304 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]